bond
Part 1: EDA
bond= read.csv('bond.csv')
bond = bond[bond$observation_date >= "1974-01-01" & bond$observation_date <= "2021-10-01", ]
bond## observation_date BAA BAA10YM AAA
## 169 1974-01-01 8.48 1.49 7.83
## 170 1974-02-01 8.53 1.57 7.85
## 171 1974-03-01 8.62 1.41 8.01
## 172 1974-04-01 8.87 1.36 8.25
## 173 1974-05-01 9.05 1.47 8.37
## 174 1974-06-01 9.27 1.73 8.47
## 175 1974-07-01 9.48 1.67 8.72
## 176 1974-08-01 9.77 1.73 9.00
## 177 1974-09-01 10.18 2.14 9.24
## 178 1974-10-01 10.48 2.58 9.27
## 179 1974-11-01 10.60 2.92 8.89
## 180 1974-12-01 10.63 3.20 8.89
## 181 1975-01-01 10.81 3.31 8.83
## 182 1975-02-01 10.65 3.26 8.62
## 183 1975-03-01 10.48 2.75 8.67
## 184 1975-04-01 10.58 2.35 8.95
## 185 1975-05-01 10.69 2.63 8.90
## 186 1975-06-01 10.62 2.76 8.77
## 187 1975-07-01 10.55 2.49 8.84
## 188 1975-08-01 10.59 2.19 8.95
## 189 1975-09-01 10.61 2.18 8.95
## 190 1975-10-01 10.62 2.48 8.86
## 191 1975-11-01 10.56 2.51 8.78
## 192 1975-12-01 10.56 2.56 8.79
## 193 1976-01-01 10.41 2.67 8.60
## 194 1976-02-01 10.24 2.45 8.55
## 195 1976-03-01 10.12 2.39 8.52
## 196 1976-04-01 9.94 2.38 8.40
## 197 1976-05-01 9.86 1.96 8.58
## 198 1976-06-01 9.89 2.03 8.62
## 199 1976-07-01 9.82 1.99 8.56
## 200 1976-08-01 9.64 1.87 8.45
## 201 1976-09-01 9.40 1.81 8.38
## 202 1976-10-01 9.29 1.88 8.32
## 203 1976-11-01 9.23 1.94 8.25
## 204 1976-12-01 9.12 2.25 7.98
## 205 1977-01-01 9.08 1.87 7.96
## 206 1977-02-01 9.12 1.73 8.04
## 207 1977-03-01 9.12 1.66 8.10
## 208 1977-04-01 9.07 1.70 8.04
## 209 1977-05-01 9.01 1.55 8.05
## 210 1977-06-01 8.91 1.63 7.95
## 211 1977-07-01 8.87 1.54 7.94
## 212 1977-08-01 8.82 1.42 7.98
## 213 1977-09-01 8.80 1.46 7.92
## 214 1977-10-01 8.89 1.37 8.04
## 215 1977-11-01 8.95 1.37 8.08
## 216 1977-12-01 8.99 1.30 8.19
## 217 1978-01-01 9.17 1.21 8.41
## 218 1978-02-01 9.20 1.17 8.47
## 219 1978-03-01 9.22 1.18 8.47
## 220 1978-04-01 9.32 1.17 8.56
## 221 1978-05-01 9.49 1.14 8.69
## 222 1978-06-01 9.60 1.14 8.76
## 223 1978-07-01 9.60 0.96 8.88
## 224 1978-08-01 9.48 1.07 8.69
## 225 1978-09-01 9.42 1.00 8.69
## 226 1978-10-01 9.59 0.95 8.89
## 227 1978-11-01 9.83 1.02 9.03
## 228 1978-12-01 9.94 0.93 9.16
## 229 1979-01-01 10.13 1.03 9.25
## 230 1979-02-01 10.08 0.98 9.26
## 231 1979-03-01 10.26 1.14 9.37
## 232 1979-04-01 10.33 1.15 9.38
## 233 1979-05-01 10.47 1.22 9.50
## 234 1979-06-01 10.38 1.47 9.29
## 235 1979-07-01 10.29 1.34 9.20
## 236 1979-08-01 10.35 1.32 9.23
## 237 1979-09-01 10.54 1.21 9.44
## 238 1979-10-01 11.40 1.10 10.13
## 239 1979-11-01 11.99 1.34 10.76
## 240 1979-12-01 12.06 1.67 10.74
## 241 1980-01-01 12.42 1.62 11.09
## 242 1980-02-01 13.57 1.16 12.38
## 243 1980-03-01 14.45 1.70 12.96
## 244 1980-04-01 14.19 2.72 12.04
## 245 1980-05-01 13.17 2.99 10.99
## 246 1980-06-01 12.71 2.93 10.58
## 247 1980-07-01 12.65 2.40 11.07
## 248 1980-08-01 13.15 2.05 11.64
## 249 1980-09-01 13.70 2.19 12.02
## 250 1980-10-01 14.23 2.48 12.31
## 251 1980-11-01 14.64 1.96 12.97
## 252 1980-12-01 15.14 2.30 13.21
## 253 1981-01-01 15.03 2.46 12.81
## 254 1981-02-01 15.37 2.18 13.35
## 255 1981-03-01 15.34 2.22 13.33
## 256 1981-04-01 15.56 1.88 13.88
## 257 1981-05-01 15.95 1.85 14.32
## 258 1981-06-01 15.80 2.33 13.75
## 259 1981-07-01 16.17 1.89 14.38
## 260 1981-08-01 16.34 1.40 14.89
## 261 1981-09-01 16.92 1.60 15.49
## 262 1981-10-01 17.11 1.96 15.40
## 263 1981-11-01 16.39 3.00 14.22
## 264 1981-12-01 16.55 2.83 14.23
## 265 1982-01-01 17.10 2.51 15.18
## 266 1982-02-01 17.18 2.75 15.27
## 267 1982-03-01 16.82 2.96 14.58
## 268 1982-04-01 16.78 2.91 14.46
## 269 1982-05-01 16.64 3.02 14.26
## 270 1982-06-01 16.92 2.62 14.81
## 271 1982-07-01 16.80 2.85 14.61
## 272 1982-08-01 16.32 3.26 13.71
## 273 1982-09-01 15.63 3.29 12.94
## 274 1982-10-01 14.73 3.82 12.12
## 275 1982-11-01 14.30 3.75 11.68
## 276 1982-12-01 14.14 3.60 11.83
## 277 1983-01-01 13.94 3.48 11.79
## 278 1983-02-01 13.95 3.23 12.01
## 279 1983-03-01 13.61 3.10 11.73
## 280 1983-04-01 13.29 2.89 11.51
## 281 1983-05-01 13.09 2.71 11.46
## 282 1983-06-01 13.37 2.52 11.74
## 283 1983-07-01 13.39 2.01 12.15
## 284 1983-08-01 13.64 1.79 12.51
## 285 1983-09-01 13.55 1.90 12.37
## 286 1983-10-01 13.46 1.92 12.25
## 287 1983-11-01 13.61 1.92 12.41
## 288 1983-12-01 13.75 1.92 12.57
## 289 1984-01-01 13.65 1.98 12.20
## 290 1984-02-01 13.59 1.75 12.08
## 291 1984-03-01 13.99 1.67 12.57
## 292 1984-04-01 14.31 1.68 12.81
## 293 1984-05-01 14.74 1.33 13.28
## 294 1984-06-01 15.05 1.49 13.55
## 295 1984-07-01 15.15 1.79 13.44
## 296 1984-08-01 14.63 1.91 12.87
## 297 1984-09-01 14.35 1.83 12.66
## 298 1984-10-01 13.94 1.78 12.63
## 299 1984-11-01 13.48 1.91 12.29
## 300 1984-12-01 13.40 1.90 12.13
## 301 1985-01-01 13.26 1.88 12.08
## 302 1985-02-01 13.23 1.72 12.13
## 303 1985-03-01 13.69 1.83 12.56
## 304 1985-04-01 13.51 2.08 12.23
## 305 1985-05-01 13.15 2.30 11.72
## 306 1985-06-01 12.40 2.24 10.94
## 307 1985-07-01 12.43 2.12 10.97
## 308 1985-08-01 12.50 2.17 11.05
## 309 1985-09-01 12.48 2.11 11.07
## 310 1985-10-01 12.36 2.12 11.02
## 311 1985-11-01 11.99 2.21 10.55
## 312 1985-12-01 11.58 2.32 10.16
## 313 1986-01-01 11.44 2.25 10.05
## 314 1986-02-01 11.11 2.41 9.67
## 315 1986-03-01 10.50 2.72 9.00
## 316 1986-04-01 10.19 2.89 8.79
## 317 1986-05-01 10.29 2.58 9.09
## 318 1986-06-01 10.34 2.54 9.13
## 319 1986-07-01 10.16 2.86 8.88
## 320 1986-08-01 10.18 3.01 8.72
## 321 1986-09-01 10.20 2.75 8.89
## 322 1986-10-01 10.24 2.81 8.86
## 323 1986-11-01 10.07 2.82 8.68
## 324 1986-12-01 9.97 2.86 8.49
## 325 1987-01-01 9.72 2.64 8.36
## 326 1987-02-01 9.65 2.40 8.38
## 327 1987-03-01 9.61 2.36 8.36
## 328 1987-04-01 10.04 2.02 8.85
## 329 1987-05-01 10.51 1.90 9.33
## 330 1987-06-01 10.52 2.12 9.32
## 331 1987-07-01 10.61 2.16 9.42
## 332 1987-08-01 10.80 2.04 9.67
## 333 1987-09-01 11.31 1.89 10.18
## 334 1987-10-01 11.62 2.10 10.52
## 335 1987-11-01 11.23 2.37 10.01
## 336 1987-12-01 11.29 2.30 10.11
## 337 1988-01-01 11.07 2.40 9.88
## 338 1988-02-01 10.62 2.41 9.40
## 339 1988-03-01 10.57 2.20 9.39
## 340 1988-04-01 10.90 2.18 9.67
## 341 1988-05-01 11.04 1.95 9.90
## 342 1988-06-01 11.00 2.08 9.86
## 343 1988-07-01 11.11 2.05 9.96
## 344 1988-08-01 11.21 1.95 10.11
## 345 1988-09-01 10.90 1.92 9.82
## 346 1988-10-01 10.41 1.61 9.51
## 347 1988-11-01 10.48 1.52 9.45
## 348 1988-12-01 10.65 1.54 9.57
## 349 1989-01-01 10.65 1.56 9.62
## 350 1989-02-01 10.61 1.44 9.64
## 351 1989-03-01 10.67 1.31 9.80
## 352 1989-04-01 10.61 1.43 9.79
## 353 1989-05-01 10.46 1.60 9.57
## 354 1989-06-01 10.03 1.75 9.10
## 355 1989-07-01 9.87 1.85 8.93
## 356 1989-08-01 9.88 1.77 8.96
## 357 1989-09-01 9.91 1.72 9.01
## 358 1989-10-01 9.81 1.80 8.92
## 359 1989-11-01 9.81 1.94 8.89
## 360 1989-12-01 9.82 1.98 8.86
## 361 1990-01-01 9.94 1.73 8.99
## 362 1990-02-01 10.14 1.67 9.22
## 363 1990-03-01 10.21 1.62 9.37
## 364 1990-04-01 10.30 1.51 9.46
## 365 1990-05-01 10.41 1.65 9.47
## 366 1990-06-01 10.22 1.74 9.26
## 367 1990-07-01 10.20 1.73 9.24
## 368 1990-08-01 10.41 1.66 9.41
## 369 1990-09-01 10.64 1.75 9.56
## 370 1990-10-01 10.74 2.02 9.53
## 371 1990-11-01 10.62 2.23 9.30
## 372 1990-12-01 10.43 2.35 9.05
## 373 1991-01-01 10.45 2.36 9.04
## 374 1991-02-01 10.07 2.22 8.83
## 375 1991-03-01 10.09 1.98 8.93
## 376 1991-04-01 9.94 1.90 8.86
## 377 1991-05-01 9.86 1.79 8.86
## 378 1991-06-01 9.96 1.68 9.01
## 379 1991-07-01 9.89 1.62 9.00
## 380 1991-08-01 9.65 1.75 8.75
## 381 1991-09-01 9.51 1.86 8.61
## 382 1991-10-01 9.49 1.96 8.55
## 383 1991-11-01 9.45 2.03 8.48
## 384 1991-12-01 9.26 2.17 8.31
## 385 1992-01-01 9.13 2.10 8.20
## 386 1992-02-01 9.23 1.89 8.29
## 387 1992-03-01 9.25 1.71 8.35
## 388 1992-04-01 9.21 1.73 8.33
## 389 1992-05-01 9.13 1.74 8.28
## 390 1992-06-01 9.05 1.79 8.22
## 391 1992-07-01 8.84 2.00 8.07
## 392 1992-08-01 8.65 2.06 7.95
## 393 1992-09-01 8.62 2.20 7.92
## 394 1992-10-01 8.84 2.25 7.99
## 395 1992-11-01 8.96 2.09 8.10
## 396 1992-12-01 8.81 2.04 7.98
## 397 1993-01-01 8.67 2.07 7.91
## 398 1993-02-01 8.39 2.13 7.71
## 399 1993-03-01 8.15 2.17 7.58
## 400 1993-04-01 8.14 2.17 7.46
## 401 1993-05-01 8.21 2.17 7.43
## 402 1993-06-01 8.07 2.11 7.33
## 403 1993-07-01 7.93 2.12 7.17
## 404 1993-08-01 7.60 1.92 6.85
## 405 1993-09-01 7.34 1.98 6.66
## 406 1993-10-01 7.31 1.98 6.67
## 407 1993-11-01 7.66 1.94 6.93
## 408 1993-12-01 7.69 1.92 6.93
## 409 1994-01-01 7.65 1.90 6.92
## 410 1994-02-01 7.76 1.79 7.08
## 411 1994-03-01 8.13 1.65 7.48
## 412 1994-04-01 8.52 1.55 7.88
## 413 1994-05-01 8.62 1.44 7.99
## 414 1994-06-01 8.65 1.55 7.97
## 415 1994-07-01 8.80 1.50 8.11
## 416 1994-08-01 8.74 1.50 8.07
## 417 1994-09-01 8.98 1.52 8.34
## 418 1994-10-01 9.20 1.46 8.57
## 419 1994-11-01 9.32 1.36 8.68
## 420 1994-12-01 9.10 1.29 8.46
## 421 1995-01-01 9.08 1.30 8.46
## 422 1995-02-01 8.85 1.38 8.26
## 423 1995-03-01 8.70 1.50 8.12
## 424 1995-04-01 8.60 1.54 8.03
## 425 1995-05-01 8.20 1.57 7.65
## 426 1995-06-01 7.90 1.73 7.30
## 427 1995-07-01 8.04 1.76 7.41
## 428 1995-08-01 8.19 1.70 7.57
## 429 1995-09-01 7.93 1.73 7.32
## 430 1995-10-01 7.75 1.71 7.12
## 431 1995-11-01 7.68 1.75 7.02
## 432 1995-12-01 7.49 1.78 6.82
## 433 1996-01-01 7.47 1.82 6.81
## 434 1996-02-01 7.63 1.82 6.99
## 435 1996-03-01 8.03 1.76 7.35
## 436 1996-04-01 8.19 1.68 7.50
## 437 1996-05-01 8.30 1.56 7.62
## 438 1996-06-01 8.40 1.49 7.71
## 439 1996-07-01 8.35 1.48 7.65
## 440 1996-08-01 8.18 1.54 7.46
## 441 1996-09-01 8.35 1.52 7.66
## 442 1996-10-01 8.07 1.54 7.39
## 443 1996-11-01 7.79 1.59 7.10
## 444 1996-12-01 7.89 1.59 7.20
## 445 1997-01-01 8.09 1.51 7.42
## 446 1997-02-01 7.94 1.52 7.31
## 447 1997-03-01 8.18 1.49 7.55
## 448 1997-04-01 8.34 1.45 7.73
## 449 1997-05-01 8.20 1.49 7.58
## 450 1997-06-01 8.02 1.53 7.41
## 451 1997-07-01 7.75 1.53 7.14
## 452 1997-08-01 7.82 1.52 7.22
## 453 1997-09-01 7.70 1.49 7.15
## 454 1997-10-01 7.57 1.54 7.00
## 455 1997-11-01 7.42 1.54 6.87
## 456 1997-12-01 7.32 1.51 6.76
## 457 1998-01-01 7.19 1.65 6.61
## 458 1998-02-01 7.25 1.68 6.67
## 459 1998-03-01 7.32 1.67 6.72
## 460 1998-04-01 7.33 1.69 6.69
## 461 1998-05-01 7.30 1.65 6.69
## 462 1998-06-01 7.13 1.63 6.53
## 463 1998-07-01 7.15 1.69 6.55
## 464 1998-08-01 7.14 1.80 6.52
## 465 1998-09-01 7.09 2.28 6.40
## 466 1998-10-01 7.18 2.65 6.37
## 467 1998-11-01 7.34 2.51 6.41
## 468 1998-12-01 7.23 2.58 6.22
## 469 1999-01-01 7.29 2.57 6.24
## 470 1999-02-01 7.39 2.39 6.40
## 471 1999-03-01 7.53 2.30 6.62
## 472 1999-04-01 7.48 2.30 6.64
## 473 1999-05-01 7.72 2.18 6.93
## 474 1999-06-01 8.02 2.12 7.23
## 475 1999-07-01 7.95 2.16 7.19
## 476 1999-08-01 8.15 2.21 7.40
## 477 1999-09-01 8.20 2.28 7.39
## 478 1999-10-01 8.38 2.27 7.55
## 479 1999-11-01 8.15 2.12 7.36
## 480 1999-12-01 8.19 1.91 7.55
## 481 2000-01-01 8.33 1.67 7.78
## 482 2000-02-01 8.29 1.77 7.68
## 483 2000-03-01 8.37 2.11 7.68
## 484 2000-04-01 8.40 2.41 7.64
## 485 2000-05-01 8.90 2.46 7.99
## 486 2000-06-01 8.48 2.38 7.67
## 487 2000-07-01 8.35 2.30 7.65
## 488 2000-08-01 8.26 2.43 7.55
## 489 2000-09-01 8.35 2.55 7.62
## 490 2000-10-01 8.34 2.60 7.55
## 491 2000-11-01 8.28 2.56 7.45
## 492 2000-12-01 8.02 2.78 7.21
## 493 2001-01-01 7.93 2.77 7.15
## 494 2001-02-01 7.87 2.77 7.10
## 495 2001-03-01 7.84 2.95 6.98
## 496 2001-04-01 8.07 2.93 7.20
## 497 2001-05-01 8.07 2.68 7.29
## 498 2001-06-01 7.97 2.69 7.18
## 499 2001-07-01 7.97 2.73 7.13
## 500 2001-08-01 7.85 2.88 7.02
## 501 2001-09-01 8.03 3.30 7.17
## 502 2001-10-01 7.91 3.34 7.03
## 503 2001-11-01 7.81 3.16 6.97
## 504 2001-12-01 8.05 2.96 6.77
## 505 2002-01-01 7.87 2.83 6.55
## 506 2002-02-01 7.89 2.98 6.51
## 507 2002-03-01 8.11 2.83 6.81
## 508 2002-04-01 8.03 2.82 6.76
## 509 2002-05-01 8.09 2.93 6.75
## 510 2002-06-01 7.95 3.02 6.63
## 511 2002-07-01 7.90 3.25 6.53
## 512 2002-08-01 7.58 3.32 6.37
## 513 2002-09-01 7.40 3.53 6.15
## 514 2002-10-01 7.73 3.79 6.32
## 515 2002-11-01 7.62 3.57 6.31
## 516 2002-12-01 7.45 3.42 6.21
## 517 2003-01-01 7.35 3.30 6.17
## 518 2003-02-01 7.06 3.16 5.95
## 519 2003-03-01 6.95 3.14 5.89
## 520 2003-04-01 6.85 2.89 5.74
## 521 2003-05-01 6.38 2.81 5.22
## 522 2003-06-01 6.19 2.86 4.97
## 523 2003-07-01 6.62 2.64 5.49
## 524 2003-08-01 7.01 2.56 5.88
## 525 2003-09-01 6.79 2.52 5.72
## 526 2003-10-01 6.73 2.44 5.70
## 527 2003-11-01 6.66 2.36 5.65
## 528 2003-12-01 6.60 2.33 5.62
## 529 2004-01-01 6.44 2.29 5.54
## 530 2004-02-01 6.27 2.19 5.50
## 531 2004-03-01 6.11 2.28 5.33
## 532 2004-04-01 6.46 2.11 5.73
## 533 2004-05-01 6.75 2.03 6.04
## 534 2004-06-01 6.78 2.05 6.01
## 535 2004-07-01 6.62 2.12 5.82
## 536 2004-08-01 6.46 2.18 5.65
## 537 2004-09-01 6.27 2.14 5.46
## 538 2004-10-01 6.21 2.11 5.47
## 539 2004-11-01 6.20 2.01 5.52
## 540 2004-12-01 6.15 1.92 5.47
## 541 2005-01-01 6.02 1.80 5.36
## 542 2005-02-01 5.82 1.65 5.20
## 543 2005-03-01 6.06 1.56 5.40
## 544 2005-04-01 6.05 1.71 5.33
## 545 2005-05-01 6.01 1.87 5.15
## 546 2005-06-01 5.86 1.86 4.96
## 547 2005-07-01 5.95 1.77 5.06
## 548 2005-08-01 5.96 1.70 5.09
## 549 2005-09-01 6.03 1.83 5.13
## 550 2005-10-01 6.30 1.84 5.35
## 551 2005-11-01 6.39 1.85 5.42
## 552 2005-12-01 6.32 1.85 5.37
## 553 2006-01-01 6.24 1.82 5.29
## 554 2006-02-01 6.27 1.70 5.35
## 555 2006-03-01 6.41 1.69 5.53
## 556 2006-04-01 6.68 1.69 5.84
## 557 2006-05-01 6.75 1.64 5.95
## 558 2006-06-01 6.78 1.67 5.89
## 559 2006-07-01 6.76 1.67 5.85
## 560 2006-08-01 6.59 1.71 5.68
## 561 2006-09-01 6.43 1.71 5.51
## 562 2006-10-01 6.42 1.69 5.51
## 563 2006-11-01 6.20 1.60 5.33
## 564 2006-12-01 6.22 1.66 5.32
## 565 2007-01-01 6.34 1.58 5.40
## 566 2007-02-01 6.28 1.56 5.39
## 567 2007-03-01 6.27 1.71 5.30
## 568 2007-04-01 6.39 1.70 5.47
## 569 2007-05-01 6.39 1.64 5.47
## 570 2007-06-01 6.70 1.60 5.79
## 571 2007-07-01 6.65 1.65 5.73
## 572 2007-08-01 6.65 1.98 5.79
## 573 2007-09-01 6.59 2.07 5.74
## 574 2007-10-01 6.48 1.95 5.66
## 575 2007-11-01 6.40 2.25 5.44
## 576 2007-12-01 6.65 2.55 5.49
## 577 2008-01-01 6.54 2.80 5.33
## 578 2008-02-01 6.82 3.08 5.53
## 579 2008-03-01 6.89 3.38 5.51
## 580 2008-04-01 6.97 3.29 5.55
## 581 2008-05-01 6.93 3.05 5.57
## 582 2008-06-01 7.07 2.97 5.68
## 583 2008-07-01 7.16 3.15 5.67
## 584 2008-08-01 7.15 3.26 5.64
## 585 2008-09-01 7.31 3.62 5.65
## 586 2008-10-01 8.88 5.07 6.28
## 587 2008-11-01 9.21 5.68 6.12
## 588 2008-12-01 8.43 6.01 5.05
## 589 2009-01-01 8.14 5.62 5.05
## 590 2009-02-01 8.08 5.21 5.27
## 591 2009-03-01 8.42 5.60 5.50
## 592 2009-04-01 8.39 5.46 5.39
## 593 2009-05-01 8.06 4.77 5.54
## 594 2009-06-01 7.50 3.78 5.61
## 595 2009-07-01 7.09 3.53 5.41
## 596 2009-08-01 6.58 2.99 5.26
## 597 2009-09-01 6.31 2.91 5.13
## 598 2009-10-01 6.29 2.90 5.15
## 599 2009-11-01 6.32 2.92 5.19
## 600 2009-12-01 6.37 2.78 5.26
## 601 2010-01-01 6.25 2.52 5.26
## 602 2010-02-01 6.34 2.65 5.35
## 603 2010-03-01 6.27 2.54 5.27
## 604 2010-04-01 6.25 2.40 5.29
## 605 2010-05-01 6.05 2.63 4.96
## 606 2010-06-01 6.23 3.03 4.88
## 607 2010-07-01 6.01 3.00 4.72
## 608 2010-08-01 5.66 2.96 4.49
## 609 2010-09-01 5.66 3.01 4.53
## 610 2010-10-01 5.72 3.18 4.68
## 611 2010-11-01 5.92 3.16 4.87
## 612 2010-12-01 6.10 2.81 5.02
## 613 2011-01-01 6.09 2.70 5.04
## 614 2011-02-01 6.15 2.57 5.22
## 615 2011-03-01 6.03 2.62 5.13
## 616 2011-04-01 6.02 2.56 5.16
## 617 2011-05-01 5.78 2.61 4.96
## 618 2011-06-01 5.75 2.75 4.99
## 619 2011-07-01 5.76 2.76 4.93
## 620 2011-08-01 5.36 3.06 4.37
## 621 2011-09-01 5.27 3.29 4.09
## 622 2011-10-01 5.37 3.22 3.98
## 623 2011-11-01 5.14 3.13 3.87
## 624 2011-12-01 5.25 3.27 3.93
## 625 2012-01-01 5.23 3.26 3.85
## 626 2012-02-01 5.14 3.17 3.85
## 627 2012-03-01 5.23 3.06 3.99
## 628 2012-04-01 5.19 3.14 3.96
## 629 2012-05-01 5.07 3.27 3.80
## 630 2012-06-01 5.02 3.40 3.64
## 631 2012-07-01 4.87 3.34 3.40
## 632 2012-08-01 4.91 3.23 3.48
## 633 2012-09-01 4.84 3.12 3.49
## 634 2012-10-01 4.58 2.83 3.47
## 635 2012-11-01 4.51 2.86 3.50
## 636 2012-12-01 4.63 2.91 3.65
## 637 2013-01-01 4.73 2.82 3.80
## 638 2013-02-01 4.85 2.87 3.90
## 639 2013-03-01 4.85 2.89 3.93
## 640 2013-04-01 4.59 2.83 3.73
## 641 2013-05-01 4.73 2.80 3.89
## 642 2013-06-01 5.19 2.89 4.27
## 643 2013-07-01 5.32 2.74 4.34
## 644 2013-08-01 5.42 2.68 4.54
## 645 2013-09-01 5.47 2.66 4.64
## 646 2013-10-01 5.31 2.69 4.53
## 647 2013-11-01 5.38 2.66 4.63
## 648 2013-12-01 5.38 2.48 4.62
## 649 2014-01-01 5.19 2.33 4.49
## 650 2014-02-01 5.10 2.39 4.45
## 651 2014-03-01 5.06 2.34 4.38
## 652 2014-04-01 4.90 2.19 4.24
## 653 2014-05-01 4.76 2.20 4.16
## 654 2014-06-01 4.80 2.20 4.25
## 655 2014-07-01 4.73 2.19 4.16
## 656 2014-08-01 4.69 2.27 4.08
## 657 2014-09-01 4.80 2.27 4.11
## 658 2014-10-01 4.69 2.39 3.92
## 659 2014-11-01 4.79 2.46 3.92
## 660 2014-12-01 4.74 2.53 3.79
## 661 2015-01-01 4.45 2.57 3.46
## 662 2015-02-01 4.51 2.53 3.61
## 663 2015-03-01 4.54 2.50 3.64
## 664 2015-04-01 4.48 2.54 3.52
## 665 2015-05-01 4.89 2.69 3.98
## 666 2015-06-01 5.13 2.77 4.19
## 667 2015-07-01 5.20 2.88 4.15
## 668 2015-08-01 5.19 3.02 4.04
## 669 2015-09-01 5.34 3.17 4.07
## 670 2015-10-01 5.34 3.27 3.95
## 671 2015-11-01 5.46 3.20 4.06
## 672 2015-12-01 5.46 3.22 3.97
## 673 2016-01-01 5.45 3.36 4.00
## 674 2016-02-01 5.34 3.56 3.96
## 675 2016-03-01 5.13 3.24 3.82
## 676 2016-04-01 4.79 2.98 3.62
## 677 2016-05-01 4.68 2.87 3.65
## 678 2016-06-01 4.53 2.89 3.50
## 679 2016-07-01 4.22 2.72 3.28
## 680 2016-08-01 4.24 2.68 3.32
## 681 2016-09-01 4.31 2.68 3.41
## 682 2016-10-01 4.38 2.62 3.51
## 683 2016-11-01 4.71 2.57 3.86
## 684 2016-12-01 4.83 2.34 4.06
## 685 2017-01-01 4.66 2.23 3.92
## 686 2017-02-01 4.64 2.22 3.95
## 687 2017-03-01 4.68 2.20 4.01
## 688 2017-04-01 4.57 2.27 3.87
## 689 2017-05-01 4.55 2.25 3.85
## 690 2017-06-01 4.37 2.18 3.68
## 691 2017-07-01 4.39 2.07 3.70
## 692 2017-08-01 4.31 2.10 3.63
## 693 2017-09-01 4.30 2.10 3.63
## 694 2017-10-01 4.32 1.96 3.60
## 695 2017-11-01 4.27 1.92 3.57
## 696 2017-12-01 4.22 1.82 3.51
## 697 2018-01-01 4.26 1.68 3.55
## 698 2018-02-01 4.51 1.65 3.82
## 699 2018-03-01 4.64 1.80 3.87
## 700 2018-04-01 4.67 1.80 3.85
## 701 2018-05-01 4.83 1.85 4.00
## 702 2018-06-01 4.83 1.92 3.96
## 703 2018-07-01 4.79 1.90 3.87
## 704 2018-08-01 4.77 1.88 3.88
## 705 2018-09-01 4.88 1.88 3.98
## 706 2018-10-01 5.07 1.92 4.14
## 707 2018-11-01 5.22 2.10 4.22
## 708 2018-12-01 5.13 2.30 4.02
## 709 2019-01-01 5.12 2.41 3.93
## 710 2019-02-01 4.95 2.27 3.79
## 711 2019-03-01 4.84 2.27 3.77
## 712 2019-04-01 4.70 2.17 3.69
## 713 2019-05-01 4.63 2.23 3.67
## 714 2019-06-01 4.46 2.39 3.42
## 715 2019-07-01 4.28 2.22 3.29
## 716 2019-08-01 3.87 2.24 2.98
## 717 2019-09-01 3.91 2.21 3.03
## 718 2019-10-01 3.92 2.21 3.01
## 719 2019-11-01 3.94 2.13 3.06
## 720 2019-12-01 3.88 2.02 3.01
## 721 2020-01-01 3.77 2.01 2.94
## 722 2020-02-01 3.61 2.11 2.78
## 723 2020-03-01 4.29 3.42 3.02
## 724 2020-04-01 4.13 3.47 2.43
## 725 2020-05-01 3.95 3.28 2.50
## 726 2020-06-01 3.64 2.91 2.44
## 727 2020-07-01 3.31 2.69 2.14
## 728 2020-08-01 3.27 2.62 2.25
## 729 2020-09-01 3.36 2.68 2.31
## 730 2020-10-01 3.44 2.65 2.35
## 731 2020-11-01 3.30 2.43 2.30
## 732 2020-12-01 3.16 2.23 2.26
## 733 2021-01-01 3.24 2.16 2.45
## 734 2021-02-01 3.42 2.16 2.70
## 735 2021-03-01 3.74 2.13 3.04
## 736 2021-04-01 3.60 1.97 2.90
## 737 2021-05-01 3.62 2.00 2.96
## 738 2021-06-01 3.44 1.92 2.79
## 739 2021-07-01 3.24 1.92 2.57
## 740 2021-08-01 3.24 1.96 2.55
## 741 2021-09-01 3.23 1.86 2.53
## 742 2021-10-01 3.35 1.77 2.68library(anytime)
bond$observation_date= anydate(bond$observation_date)class(bond$observation_date)## [1] "Date"baa = bond[,2]
aaa = bond[,4]
spread = bond$BAA10YM
plot(baa ~ bond$observation_date, type = "l", main = "Baa Monthly Corporate Bond Yield")
plot(aaa~ bond$observation_date, type = "l", main = "AAA Monthly Corporate Bond Yield")
kpss test
kpss.test(baa, null = "Trend")## Warning in kpss.test(baa, null = "Trend"): p-value smaller than printed p-value##
## KPSS Test for Trend Stationarity
##
## data: baa
## KPSS Trend = 0.34773, Truncation lag parameter = 6, p-value = 0.01kpss.test(aaa, null = "Trend")## Warning in kpss.test(aaa, null = "Trend"): p-value smaller than printed p-value##
## KPSS Test for Trend Stationarity
##
## data: aaa
## KPSS Trend = 0.42069, Truncation lag parameter = 6, p-value = 0.01kpss.test(spread, null = "Trend")##
## KPSS Test for Trend Stationarity
##
## data: spread
## KPSS Trend = 0.17893, Truncation lag parameter = 6, p-value = 0.0239non stationary even after removing trends
plot(spread~ bond$observation_date, type = "l", main = "Credit Spread")
baa_aaa = lm(baa~ aaa, data=bond)
summary(baa_aaa)##
## Call:
## lm(formula = baa ~ aaa, data = bond)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.56865 -0.28162 -0.07694 0.17943 2.43516
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.623325 0.046503 13.4 <2e-16 ***
## aaa 1.063667 0.005947 178.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4112 on 572 degrees of freedom
## Multiple R-squared: 0.9824, Adjusted R-squared: 0.9824
## F-statistic: 3.199e+04 on 1 and 572 DF, p-value: < 2.2e-16baa_credit = lm(baa~ spread, data=bond)
summary(baa_credit)##
## Call:
## lm(formula = baa ~ spread, data = bond)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.3500 -2.2905 -0.2308 1.6943 9.1119
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.6498 0.4293 22.476 < 2e-16 ***
## spread -0.5751 0.1817 -3.165 0.00164 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.076 on 572 degrees of freedom
## Multiple R-squared: 0.01721, Adjusted R-squared: 0.01549
## F-statistic: 10.01 on 1 and 572 DF, p-value: 0.001636acf(baa)
pacf(baa)
acf(spread)
pacf(spread)
plot(baa_aaa$residuals)
plot(baa_credit$residuals)
bond$aaa_spread = bond$BAA - bond$AAA
aaa_spread = bond$aaa_spreadplot(bond$aaa_spread~ bond$observation_date, type = "l", main = "Spread Against AAA Monthly Corporate Bond Yield")
acf(aaa_spread)
pacf(aaa_spread)
aaa_spread_lm = lm(baa~aaa_spread)
summary(aaa_spread_lm)##
## Call:
## lm(formula = baa ~ aaa_spread)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.2317 -2.1294 0.5891 1.9212 7.3208
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.4200 0.2879 15.35 <2e-16 ***
## aaa_spread 3.6218 0.2449 14.79 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.639 on 572 degrees of freedom
## Multiple R-squared: 0.2766, Adjusted R-squared: 0.2753
## F-statistic: 218.7 on 1 and 572 DF, p-value: < 2.2e-16plot(aaa_spread_lm$residuals)
library(forecast)
arima_baa = auto.arima(baa)acf(arima_baa$residuals)
pacf(arima_baa$residuals)
plot(arima_baa$residuals)
arima_spread = auto.arima(spread)
arima_spread## Series: spread
## ARIMA(2,1,4)
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 ma4
## -0.5144 -0.6045 0.8904 0.7457 0.1461 -0.1585
## s.e. 0.1910 0.1687 0.1892 0.1599 0.0835 0.0440
##
## sigma^2 = 0.0347: log likelihood = 152.76
## AIC=-291.52 AICc=-291.32 BIC=-261.06acf(arima_spread$residuals)
pacf(arima_spread$residuals)
plot(arima_spread$residuals)
heteroskedasticity tests
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericBox.test(arima_baa$residuals, type= "Ljung")##
## Box-Ljung test
##
## data: arima_baa$residuals
## X-squared = 0.27531, df = 1, p-value = 0.5998Box.test(arima_spread$residuals, type= "Ljung")##
## Box-Ljung test
##
## data: arima_spread$residuals
## X-squared = 0.0033439, df = 1, p-value = 0.9539Part 2: Fitting Model
train test split
train = bond[bond$observation_date >= "1974-01-01" & bond$observation_date <= "2020-10-01",][,1:2]
test = bond[bond$observation_date >= "2020-11-01" & bond$observation_date <= "2021-10-01",][,1:2]train_aaa_temp = bond[bond$observation_date >= "1974-01-01" & bond$observation_date <= "2020-10-01",]
train_aaa = train_aaa_temp$AAA
test_aaa_temp = bond[bond$observation_date >= "2020-11-01" & bond$observation_date <= "2021-10-01",]
test_aaa = test_aaa_temp$AAAtrain_baa_temp = bond[bond$observation_date >= "1974-01-01" & bond$observation_date <= "2020-10-01",]
train_baa = train_baa_temp$BAA
test_baa_temp = bond[bond$observation_date >= "2020-11-01" & bond$observation_date <= "2021-10-01",]
test_baa = test_baa_temp$BAAbaa_train1 <- bond[bond$observation_date >= "1974-01-01" & bond$observation_date <= "2016-10-01",]$BAA
baa_val1 <- bond[bond$observation_date >= "2016-11-01" & bond$observation_date <= "2017-10-01",]$BAA
baa_train2 <- bond[bond$observation_date >= "1975-01-01" & bond$observation_date <= "2017-10-01",]$BAA
baa_val2 <- bond[bond$observation_date >= "2017-11-01" & bond$observation_date <= "2018-10-01",]$BAA
baa_train3 <- bond[bond$observation_date >= "1976-11-01" & bond$observation_date <= "2018-10-01",]$BAA
baa_val3 <- bond[bond$observation_date >= "2018-11-01" & bond$observation_date <= "2019-10-01",]$BAA aaa_train1 <- bond[bond$observation_date >= "1974-01-01" & bond$observation_date <= "2016-10-01",]$AAA
aaa_val1 <- bond[bond$observation_date >= "2016-11-01" & bond$observation_date <= "2017-10-01",]$AAA
aaa_train2 <- bond[bond$observation_date >= "1975-01-01" & bond$observation_date <= "2017-10-01",]$AAA
aaa_val2 <- bond[bond$observation_date >= "2017-11-01" & bond$observation_date <= "2018-10-01",]$AAA
aaa_train3 <- bond[bond$observation_date >= "1976-11-01" & bond$observation_date <= "2018-10-01",]$AAA
aaa_val3 <- bond[bond$observation_date >= "2018-11-01" & bond$observation_date <= "2019-10-01",]$AAA Cointegration
Granger Causality Test
library(lmtest)grangertest(aaa, baa, order = 2)## Granger causality test
##
## Model 1: baa ~ Lags(baa, 1:2) + Lags(aaa, 1:2)
## Model 2: baa ~ Lags(baa, 1:2)
## Res.Df Df F Pr(>F)
## 1 567
## 2 569 -2 9.6043 7.907e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1at 0.05 significance level, we reject the null hypothesis that aaa does not granger - cause baa; it is reasonable to use aaa yield to predict baa
grangertest(baa, aaa, order = 2)## Granger causality test
##
## Model 1: aaa ~ Lags(aaa, 1:2) + Lags(baa, 1:2)
## Model 2: aaa ~ Lags(aaa, 1:2)
## Res.Df Df F Pr(>F)
## 1 567
## 2 569 -2 5.1047 0.00635 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#install.packages("dynlm")
library(dynlm)coint_model = dynlm(baa~aaa)
summary(coint_model)##
## Time series regression with "numeric" data:
## Start = 1, End = 574
##
## Call:
## dynlm(formula = baa ~ aaa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.56865 -0.28162 -0.07694 0.17943 2.43516
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.623325 0.046503 13.4 <2e-16 ***
## aaa 1.063667 0.005947 178.9 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4112 on 572 degrees of freedom
## Multiple R-squared: 0.9824, Adjusted R-squared: 0.9824
## F-statistic: 3.199e+04 on 1 and 572 DF, p-value: < 2.2e-16res_coint_model = residuals(coint_model)library(urca)
ur.df(res_coint_model)##
## ###############################################################
## # Augmented Dickey-Fuller Test Unit Root / Cointegration Test #
## ###############################################################
##
## The value of the test statistic is: -5.383reject the null hypothesis - there is cointegration relationship
Predicting using cointegration model
ts_baa_train = ts(baa, start = c(1974,1), end = c(2020,9), frequency = 12)
ts_baa_test = ts(baa, start = c(2020,10), end = c(2021,10), frequency = 12)
ts_aaa_train = ts(aaa, start = c(1974,1), end = c(2020,9), frequency = 12)
ts_aaa_test = ts(aaa, start = c(2020,10), end = c(2021,11), frequency = 12)data <- cbind(train_baa,train_aaa)
cajo <- ca.jo(data, ecdet = "none", type="eigen", K=2, spec="longrun")
summary(cajo)##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: maximal eigenvalue statistic (lambda max) , with linear trend
##
## Eigenvalues (lambda):
## [1] 0.0431781498 0.0008714339
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 1 | 0.49 6.50 8.18 11.65
## r = 0 | 24.72 12.91 14.90 19.19
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## train_baa.l2 train_aaa.l2
## train_baa.l2 1.000000 1.00000
## train_aaa.l2 -1.071817 2.01103
##
## Weights W:
## (This is the loading matrix)
##
## train_baa.l2 train_aaa.l2
## train_baa.d -0.051368166 -0.0006448633
## train_aaa.d 0.003724489 -0.0007780494fitting a Vector Error Correction Model
library(Metrics)##
## Attaching package: 'Metrics'## The following object is masked from 'package:forecast':
##
## accuracylibrary(tsDyn)##
## Attaching package: 'tsDyn'## The following object is masked from 'package:Metrics':
##
## mseVECM_tsDyn = VECM(cbind(train_baa, train_aaa), lag=2, r=1,estim = "ML")
VECM_predict= VECM_tsDyn$residuals[,1]+ train_baa## Warning in VECM_tsDyn$residuals[, 1] + train_baa: longer object length is not a
## multiple of shorter object lengthmatplot(cbind(VECM_predict, train_baa), type="l")
legend("topright",legend=c("Forecast train","Actual train"),
col=c("black","red"), lty=1:5
)
smape(VECM_predict, train_baa)## [1] 0.01893392plot(VECM_tsDyn$residuals[,1], type="l")
hist(VECM_tsDyn$residuals[,1])
library(Metrics)
predvecm<-predict(VECM_tsDyn, n.ahead=12)
smape(predvecm[,1], test_baa)## [1] 0.06148065Box.test(VECM_tsDyn$residuals[,1], type= "Ljung")##
## Box-Ljung test
##
## data: VECM_tsDyn$residuals[, 1]
## X-squared = 0.0098522, df = 1, p-value = 0.9209cross validation
VECM_val1 = VECM(cbind(baa_train1, aaa_train1), lag=2, r=1,estim = "ML")
VECM_predict_val1= VECM_val1$residuals[,1]+ baa_train1## Warning in VECM_val1$residuals[, 1] + baa_train1: longer object length is not a
## multiple of shorter object lengthsmape(VECM_predict_val1, baa_train1)## [1] 0.01808547library(Metrics)
predvecm1<-predict(VECM_val1, n.ahead=12)
smape(predvecm1[,1], baa_val1)## [1] 0.04835616VECM_val2 = VECM(cbind(baa_train2, aaa_train2), lag=2, r=1,estim = "ML")
VECM_predict_val2= VECM_val2$residuals[,1]+ baa_train2## Warning in VECM_val2$residuals[, 1] + baa_train2: longer object length is not a
## multiple of shorter object lengthsmape(VECM_predict_val2, baa_train2)## [1] 0.01813966predvecm2<-predict(VECM_val2, n.ahead=12)
smape(predvecm2[,1], baa_val2)## [1] 0.09038143VECM_val3 = VECM(cbind(baa_train3, aaa_train3), lag=2, r=1,estim = "ML")
VECM_predict_val3= VECM_val3$residuals[,1]+ baa_train3## Warning in VECM_val3$residuals[, 1] + baa_train3: longer object length is not a
## multiple of shorter object lengthsmape(VECM_predict_val3, baa_train3)## [1] 0.01859679predvecm3<-predict(VECM_val3, n.ahead=12)
smape(predvecm3[,1], baa_val3)## [1] 0.1018124Prophet
#install.packages("prophet")
library(prophet)## Loading required package: Rcpp## Loading required package: rlang##
## Attaching package: 'rlang'## The following object is masked from 'package:Metrics':
##
## llcolnames(train) <- c("ds", "y")
m = prophet(train)## Disabling weekly seasonality. Run prophet with weekly.seasonality=TRUE to override this.## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.future <- make_future_dataframe(m, periods = 12)
forecast <- predict(m, future)plot(m, forecast)
the fit doesn’t look good; try multivarate by adding AAA yield instead
multivariate
train$AAA= train_aaa
m=prophet(yearly.seasonality = T)
m <- add_regressor(m, 'AAA')
m <- fit.prophet(m, train)## Disabling weekly seasonality. Run prophet with weekly.seasonality=TRUE to override this.## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.future$AAA = bond[1:574,4]
forecast <- predict(m, future)multivariate prophet evaluation - only add aaa
plot(m,forecast)
prophet_plot_components(m, forecast)
library(Metrics)
prophet_predicted = forecast$yhat
length(prophet_predicted)## [1] 574residuals_prophet = bond$BAA - prophet_predicted
plot(residuals_prophet, type="l")
hist(residuals_prophet)
smape(bond$BAA, prophet_predicted)## [1] 0.0310414smape(test_baa, tail(prophet_predicted,12))## [1] 0.02539711Box.test(residuals_prophet, type= "Ljung")##
## Box-Ljung test
##
## data: residuals_prophet
## X-squared = 483.5, df = 1, p-value < 2.2e-16